Please take a look at the images and tell me if there are any way to have a perfect transition between colors and get rid of that noise marked in the last image.
There is a way to make that plane receive the sphere shadow with the plane's darker color (dark pink)? The way it is now, the sphere has no projected shadow.
(I created the plane's material the same way I created the sphere, but with just two color instead of four)
The problem is caused by the geometry at the pole of the UV Sphere interacting with the Smooth Shading to produce artifacts in the generated Normal as described in this question and its associated answers : How to avoid the wrinkle at the poles of the UV sphere?
The UV Sphere consists of edges formed from the Latitudinal lines (those around the sphere) and the Longitudinal lines (those going north to south). The Longitudinal lines all converge at the poles and this creates a number of long thin triangle faces as shown :
The problem is that slight inaccuracies in the smooth shading of each adjacent face is resulting in noticeable artifacts in your toon shader.
You can avoid this problem by changing the geometry to avoid such long thin triangular faces. The attached answers provide some methods of achieving this but an alternative is to use an Ico Sphere in place of a UV Sphere.
The geometry of an Ico Sphere is made up by subdividing an Icosahedron (a 20-sided regular mesh) such that each face is an equilateral triangle. As there is no 'pole' to provide difficult geometry you should no longer get the issue.
Once you have created the Ico Sphere you can adjust the number of sub-divisions to determine the level of detail.
Setting the mesh to Smooth Shading should produce a consistently smooth sphere.
For the shadows you could simply use the Shadow output of the existing Lamp Data node as the factor to a MixRGB node set to Multiply by a light grey (vary the intensity of this grey to affect the density of the shadow) as shown :
